Problem: If $x \bigtriangleup y = 5x+y$ and $x \boxdot y = 4x^{2}+y^{2}$, find $2 \boxdot (1 \bigtriangleup -4)$.
First, find $1 \bigtriangleup -4$ $ 1 \bigtriangleup -4 = (5)(1)-4$ $ \hphantom{1 \bigtriangleup -4} = 1$ Now, find $2 \boxdot 1$ $ 2 \boxdot 1 = 4(2^{2})+1^{2}$ $ \hphantom{2 \boxdot 1} = 17$.